If the arc length and chord length between two points (two points on a circle that constitute a minor arc ) in a circle are known , find radius of the circle?
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What level of geometry do you know? Trigonometric functions? – TZakrevskiy Mar 16 '14 at 11:10
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If the $O$ is the center of the circle, $A$ and $B$ are the end points of the chord and arc, then et $\alpha$ be an angle $\angle AOB$.
Let also $c$ - the length of the arc and $b$ - the length of $AB$, $d$ - diameter. Then we know that $$\alpha d/2 = c,$$ $$d\sin (\alpha/2)=b,$$ or $$ \sin \left(\frac{c}{d}\right)=\frac bd.$$ If $x = \frac cd$, then you are to solve an equation $$\sin x = \frac bc x.$$
TonyK
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TZakrevskiy
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@eagleseye: Numerical methods are appropriate. See more about the (unnormalized) sinc or cardinal sine function. The Question I linked above led to this earlier discussion of numerical methods of solution. – hardmath Jun 03 '14 at 06:28